Sharp Integral Inequalities of the Hermite–Hadamard Type |
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Authors: | Allal Guessab Gerhard Schmeisser |
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Affiliation: | Department of Applied Mathematics, University of Pau, 64000, Pau, Francef1;Mathematical Institute, University of Erlangen–Nuremberg, Bismarckstrasse 1 1/2, D-91054, Erlangen, Germany, f2 |
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Abstract: | We consider a family of two-point quadrature formulae and establish sharp estimates for the remainders under various regularity conditions. Improved forms of certain integral inequalities due to Hermite and Hadamard, Iyengar, Milovanovi and Pecari, and others are obtained as special cases. Our results can also be interpreted as analogues to a theorem of Ostrowski on the deviation of a function from its averages. Furthermore, we establish a generalization of a result of Fink concerning Lp estimates for the remainder of the trapezoidal rule and present the best constants in the error bounds. |
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Keywords: | Hermite– Hadamard inequality two-point quadrature Lipschitz classes Lp estimates |
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